Hierarchical Modeling for the Social Sciences
Marijtje van Duijn
Course description
In many cases data collected by social scientists exhibit some form of clustering or hierarchical structure, due to sampling (students within classes) or other longitudinal or nested designs (measurements of subjects over time). The resulting complex variance structure requires (regression) models that take into account multiple sources of variability. Hierarchical linear modeling, also known as multilevel analysis provides the appropriate methodology, and is applied extensively in the social sciences.
The goal of the course is not only to achieve a good understanding of the hierarchical models and their statistical intricacies, but also to have practical experience in applying multilevel modeling. Several commercial packages are available for this latter purpose, but in the course the free software R will be used.
Prerequisites
It is assumed that students have completed a statistical sequence (such as SOC 424-426), and a regression or an applied regression course (such as CS&SS 504). It is also recommended that students have some familiarity with basic calculus (differentiation and integration), matrix algebra (matrix addition, multiplications, and inversion), and probability theory. Some familiarity with computing packages R or S-Plus would be helpful as well.
Structure of the Course
There will be a two lectures per week. The lecture on Thursday will sometimes be a laboratory session.
Textbooks
Tom Snijders and Roel Bosker (1999). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. London: Sage Required.
José C. Pinheiro and Douglas M. Bates (2000). Mixed-Effects Models in S and S-PLUS. New York, NY: Springer. Required.
Optional texts
Agresti, A. (2002). Categorical Data Analysis. New York, NY: John Wiley & Sons.
Faraway, J.J. (2005). Linear Models with R. Boca Raton, FL: Chapman & Hall/CRC. An older version available online at http://cran.us.r-project.org/doc/contrib/Faraway-PRA.pdf
Hox, J. (2002). Multilevel models. Mahwah, NJ: Lawrence Erlbaum Associates.
Raudenbush, S.W., & Bryk, A.S. Hierarchical Linear Models: Applications and Data Analysis Methods. 2nd Edition. Thousand Oaks, CA: Sage.
Singer, J.D., & Willett, J.B. (2003). Applied Longitudinal Data Analysis. Modeling change and Event Occurrence. New York, NY: Oxford University Press.
Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models. Boca Raton, FL: Chapman & Hall/CRC.
Venables, W.N., Smith, D.M., & the R Development Core Team (2004). An Introduction to R. Revised and updated. Bristol: Network Theory Ltd. Also available online at http://www.r-project.org/
Verbeke, G. & Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. New York, NY: Springer.
Computer Usage and Software
The R/S-plus software will be used for data exploration and analysis. Other available software for hierarchical linear modeling or multilevel analysis may be used as well. See links for further information.
Course Requirements and Grades
There will be a number of homework assignments and exercises both the theory and real data analysis. Students will be graded on a scale of 1 to 10 for each assignment. This will be 50% of the grade. Homework that is not handed in on time will receive no points.
Although it is allowed to discuss homework problems with others, each student is required to prepare and submit solutions (including computer work) to the assignments and project on their own; solutions prepared “in committee” are not acceptable. Duplication of homework solutions and computer output prepared in whole or in part by someone else is not acceptable and is considered plagiarism.
There will be a final take home exam worth 50% of the grade. This can be exchanged for a project entailing a complete analysis of a data set that you may have access to. If you prefer to do such a project, get in touch with me at an early stage so that we can work out the details.
Please use a text editor to type up your homework assignments. Unless specifically requested, never submit raw computer output pages, but cut out the appropriate parts and neatly tape it onto your homework paper, or cut-and-paste it in your write-up. Be sure to use correct labels or titles for all tables, plots, etc.
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